University Of The Witwatersrand
Department Of Computational And Applied Mathematics
Masters’ Dissertation
2015 / The ideal hitting location on a cricket bat, the ‘sweet-spot’, is taken to be
defined in two parts: 1) the Location of Impact on a cricket bat that transfers
the maximum amount of energy into the batted ball and 2) the Location
of Impact that transfers the least amount of energy to the batsman’s
hands post-impact with the ball; minimizing the unpleasant stinging sensation
felt by the batsman in his hands. An analysis of di↵erent hitting
locations on a cricket bat is presented with the cricket bat modelled as a
one dimensional beam which is approximated by the Euler-Lagrange Beam
Equation. The beam is assumed to have uniform density and constant flexural
rigidity. These assumptions allow for the Euler-Lagrange Beam Equation
to be simplified considerably and hence solved numerically. The solution is
presented via both a Central Time, Central Space finite di↵erence scheme
and a Crank-Nicolson scheme. Further, the simplified Euler-Lagrange Beam
Equation is solved analytically using a Separation of Variables approach.
Boundary conditions, initial conditions and the framework of various collision
scenarios between the bat and ball are structured in such a way that the
model approximates a batsman playing a defensive cricket shot in the first
two collision scenarios and an aggressive shot in the third collision scenario.
The first collision scenario models a point-like, impulsive, perpendicular collision
between the bat and ball. A circular Hertzian pressure distribution is
used to model an elastic, perpendicular collision between the bat and ball in
the second collision scenario, and an elliptical Hertzian pressure distribution
does similarly for an elastic, oblique collision in the third collision scenario.
The pressure distributions are converted into initial velocity distributions
through the use of the Lagrange Field Equation. The numerical solution via
the Crank-Nicolson scheme and the analytical solution via the Separation
of Variables approach are analysed. For di↵erent Locations of Impact along
the length on a cricket bat, a post-impact analysis of the displacement of
points along the bat and the strain energy in the bat is conducted. Further,
through the use of a Fourier Transform, a post-impact frequency analysis
of the signals travelling in the cricket bat is performed. Combining the results
of these analyses and the two-part definition of a ‘sweet-spot’ allows
for the conclusion to be drawn that a Location of Impact as close as possible
to the fixed-end of the cricket bat (a point just below the handle of the
bat) results in minimum amount of energy transferred to the hands of the
batsman. This minimizes the ‘stinging’ sensation felt by the batsman in his
hands and satisfies the second part of the definition of a sweet-spot. Due to
the heavy emphasis of the frequency analysis in this study, the conclusion
is drawn that bat manufacturers should consider the vibrational properties
of bats more thoroughly in bat manufacturing. Further, it is concluded that
the solutions from the numerical Crank-Nicolson scheme and the analytical
Separation of Variables approach are in close agreement.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21020 |
| Date | 13 September 2016 |
| Creators | Rogers, Langton |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (116 pages), application/pdf, application/pdf |
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